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itk::KernelTransform2

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#include <itkKernelTransform2.h>

Inherits from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >, Transform< TScalarType, 3, 3 >

Public Types

Name
typedef KernelTransform2 Self
typedef AdvancedTransform< TScalarType, NDimensions, NDimensions > Superclass
typedef SmartPointer< Self > Pointer
typedef SmartPointer< const Self > ConstPointer
typedef Superclass::ScalarType ScalarType
typedef Superclass::ParametersType ParametersType
typedef Superclass::NumberOfParametersType NumberOfParametersType
typedef Superclass::JacobianType JacobianType
typedef Superclass::InputPointType InputPointType
typedef Superclass::OutputPointType OutputPointType
typedef Superclass::InputVectorType InputVectorType
typedef Superclass::OutputVectorType OutputVectorType
typedef Superclass::InputCovariantVectorType InputCovariantVectorType
typedef Superclass::OutputCovariantVectorType OutputCovariantVectorType
typedef Superclass::InputVnlVectorType InputVnlVectorType
typedef Superclass::OutputVnlVectorType OutputVnlVectorType
typedef Superclass::NonZeroJacobianIndicesType NonZeroJacobianIndicesType
typedef Superclass::SpatialJacobianType SpatialJacobianType
typedef Superclass::JacobianOfSpatialJacobianType JacobianOfSpatialJacobianType
typedef Superclass::SpatialHessianType SpatialHessianType
typedef Superclass::JacobianOfSpatialHessianType JacobianOfSpatialHessianType
typedef Superclass::InternalMatrixType InternalMatrixType
typedef DefaultStaticMeshTraits< TScalarType, NDimensions, NDimensions, TScalarType, TScalarType > PointSetTraitsType
typedef PointSet< InputPointType, NDimensions, PointSetTraitsType > PointSetType
typedef PointSetType::Pointer PointSetPointer
typedef PointSetType::PointsContainer PointsContainer
typedef PointSetType::PointsContainerIterator PointsIterator
typedef PointSetType::PointsContainerConstIterator PointsConstIterator
typedef VectorContainer< unsigned long, InputVectorType > VectorSetType
typedef VectorSetType::Pointer VectorSetPointer
typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > IMatrixType
typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > GMatrixType
typedef vnl_matrix< TScalarType > LMatrixType
typedef vnl_matrix< TScalarType > KMatrixType
typedef vnl_matrix< TScalarType > PMatrixType
typedef vnl_matrix< TScalarType > YMatrixType
typedef vnl_matrix< TScalarType > WMatrixType
typedef vnl_matrix< TScalarType > DMatrixType
typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > AMatrixType
typedef vnl_vector_fixed< TScalarType, NDimensions > BMatrixType
typedef vnl_matrix_fixed< TScalarType, 1, NDimensions > RowMatrixType
typedef vnl_matrix_fixed< TScalarType, NDimensions, 1 > ColumnMatrixType

Protected Types

Name
typedef vnl_svd< ScalarType > SVDDecompositionType
typedef vnl_qr< ScalarType > QRDecompositionType

Public Functions

Name
itkTypeMacro(KernelTransform2 , AdvancedTransform )
itkNewMacro(Self )
itkStaticConstMacro(SpaceDimension , unsigned int , NDimensions )
virtual NumberOfParametersType GetNumberOfParameters(void ) const
itkGetObjectMacro(SourceLandmarks , PointSetType )
virtual void SetSourceLandmarks(PointSetType * )
itkGetObjectMacro(TargetLandmarks , PointSetType )
virtual void SetTargetLandmarks(PointSetType * )
itkGetObjectMacro(Displacements , VectorSetType )
void ComputeWMatrix(void )
void ComputeLInverse(void )
virtual OutputPointType TransformPoint(const InputPointType & thisPoint) const
virtual OutputVectorType TransformVector(const InputVectorType & ) const
virtual OutputVnlVectorType TransformVector(const InputVnlVectorType & ) const
virtual OutputCovariantVectorType TransformCovariantVector(const InputCovariantVectorType & ) const
virtual void GetJacobian(const InputPointType & , JacobianType & , NonZeroJacobianIndicesType & ) const
virtual void SetIdentity(void )
virtual void SetParameters(const ParametersType & )
virtual void SetFixedParameters(const ParametersType & )
virtual void UpdateParameters(void )
virtual const ParametersType & GetParameters(void ) const
virtual const ParametersType & GetFixedParameters(void ) const
virtual void SetStiffness(double stiffness)
itkGetMacro(Stiffness , double )
virtual void SetAlpha(TScalarType itkNotUsedAlpha)
virtual TScalarType GetAlpha(void ) const
itkSetMacro(PoissonRatio , TScalarType )
virtual const TScalarType GetPoissonRatio(void ) const
itkSetMacro(MatrixInversionMethod , std::string )
itkGetConstReferenceMacro(MatrixInversionMethod , std::string )
virtual void GetSpatialJacobian(const InputPointType & ipp, SpatialJacobianType & sj) const
virtual void GetSpatialHessian(const InputPointType & ipp, SpatialHessianType & sh) const
virtual void GetJacobianOfSpatialJacobian(const InputPointType & ipp, JacobianOfSpatialJacobianType & jsj, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const
virtual void GetJacobianOfSpatialJacobian(const InputPointType & ipp, SpatialJacobianType & sj, JacobianOfSpatialJacobianType & jsj, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const
virtual void GetJacobianOfSpatialHessian(const InputPointType & ipp, JacobianOfSpatialHessianType & jsh, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const
virtual void GetJacobianOfSpatialHessian(const InputPointType & ipp, SpatialHessianType & sh, JacobianOfSpatialHessianType & jsh, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const

Protected Functions

Name
KernelTransform2()
virtual ~KernelTransform2()
void PrintSelf(std::ostream & os, Indent indent) const
virtual void ComputeG(const InputVectorType & landmarkVector, GMatrixType & GMatrix) const
virtual void ComputeReflexiveG(PointsIterator , GMatrixType & GMatrix) const
virtual void ComputeDeformationContribution(const InputPointType & inputPoint, OutputPointType & result) const
void ComputeK(void )
void ComputeL(void )
void ComputeP(void )
void ComputeY(void )
void ComputeD(void )
void ReorganizeW(void )

Public Attributes

Name
PointSetPointer m_SourceLandmarks
PointSetPointer m_TargetLandmarks

Protected Attributes

Name
double m_Stiffness
VectorSetPointer m_Displacements
LMatrixType m_LMatrix
LMatrixType m_LMatrixInverse
KMatrixType m_KMatrix
PMatrixType m_PMatrix
YMatrixType m_YMatrix
WMatrixType m_WMatrix
DMatrixType m_DMatrix
AMatrixType m_AMatrix
BMatrixType m_BVector
bool m_WMatrixComputed
bool m_LMatrixComputed
bool m_LInverseComputed
bool m_LMatrixDecompositionComputed
SVDDecompositionType * m_LMatrixDecompositionSVD
QRDecompositionType * m_LMatrixDecompositionQR
IMatrixType m_I
NonZeroJacobianIndicesType m_NonZeroJacobianIndices
NonZeroJacobianIndicesType m_NonZeroJacobianIndicesTemp
bool m_FastComputationPossible

Additional inherited members

Public Types inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >

Name
typedef Superclass::ParametersValueType ParametersValueType
typedef Superclass::DerivativeType DerivativeType
typedef Superclass::InverseTransformBaseType InverseTransformBaseType
typedef Superclass::InverseTransformBasePointer InverseTransformBasePointer
typedef Transform< TScalarType, NInputDimensions, NOutputDimensions > TransformType
typedef TransformType::Pointer TransformTypePointer
typedef TransformType::ConstPointer TransformTypeConstPointer
typedef OutputCovariantVectorType MovingImageGradientType
typedef MovingImageGradientType::ValueType MovingImageGradientValueType

Public Functions inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >

Name
virtual NumberOfParametersType GetNumberOfNonZeroJacobianIndices(void ) const
itkGetConstMacro(HasNonZeroSpatialHessian , bool )
itkGetConstMacro(HasNonZeroJacobianOfSpatialHessian , bool )
virtual void EvaluateJacobianWithImageGradientProduct(const InputPointType & ipp, const MovingImageGradientType & movingImageGradient, DerivativeType & imageJacobian, NonZeroJacobianIndicesType & nonZeroJacobianIndices) const
virtual void ComputeJacobianWithRespectToParameters(const InputPointType & itkNotUsedp, JacobianType & itkNotUsedj) const
virtual void ComputeJacobianWithRespectToPosition(const InputPointType & itkNotUsedp, JacobianType & itkNotUsedj) const

Protected Functions inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >

Name
AdvancedTransform()
AdvancedTransform(NumberOfParametersType numberOfParameters)
virtual ~AdvancedTransform()

Protected Attributes inherited from itk::AdvancedTransform< TScalarType, NDimensions, NDimensions >

Name
bool m_HasNonZeroSpatialHessian
bool m_HasNonZeroJacobianOfSpatialHessian

Detailed Description

template <class TScalarType ,
unsigned int NDimensions>
class itk::KernelTransform2;

Intended to be a base class for elastic body spline and thin plate spline. This is implemented in as straightforward a manner as possible from the IEEE TMI paper by Davis, Khotanzad, Flamig, and Harms, Vol. 16, No. 3 June 1997. Notation closely follows their paper, so if you have it in front of you, this code will make a lot more sense.

KernelTransform2: Provides support for defining source and target landmarks Defines a number of data types used in the computations Defines the mathematical framework used to compute all splines, so that subclasses need only provide a kernel specific to that spline

This formulation allows the stiffness of the spline to be adjusted, allowing the spline to vary from interpolating the landmarks to approximating the landmarks. This part of the formulation is based on the short paper by R. Sprengel, K. Rohr, H. Stiehl. "Thin-Plate Spline Approximation for Image Registration". In 18th International Conference of the IEEE Engineering in Medicine and Biology Society. 1996.

This class was modified to support its use in the ITK registration framework by Rupert Brooks, McGill Centre for Intelligent Machines, Montreal, Canada March 2007. See the Insight Journal Paper by Brooks, R., Arbel, T. "Improvements to the itk::KernelTransform and its subclasses."

Modified to include it in elastix:

  • style
  • make it inherit from AdvancedTransform
  • make it threadsafe, like was done in the itk as well.
  • Support for matrix inversion by QR decomposition, instead of SVD. QR is much faster. Used in SetParameters() and SetFixedParameters().
  • Much faster Jacobian computation for some of the derived kernel transforms.

Public Types Documentation

typedef Self

typedef KernelTransform2 itk::KernelTransform2< TScalarType, NDimensions >::Self;

Standard class typedefs.

typedef Superclass

typedef AdvancedTransform< TScalarType, NDimensions, NDimensions > itk::KernelTransform2< TScalarType, NDimensions >::Superclass;

typedef Pointer

typedef SmartPointer< Self > itk::KernelTransform2< TScalarType, NDimensions >::Pointer;

typedef ConstPointer

typedef SmartPointer< const Self > itk::KernelTransform2< TScalarType, NDimensions >::ConstPointer;

typedef ScalarType

typedef Superclass::ScalarType itk::KernelTransform2< TScalarType, NDimensions >::ScalarType;

Typedefs.

typedef ParametersType

typedef Superclass::ParametersType itk::KernelTransform2< TScalarType, NDimensions >::ParametersType;

typedef NumberOfParametersType

typedef Superclass::NumberOfParametersType itk::KernelTransform2< TScalarType, NDimensions >::NumberOfParametersType;

typedef JacobianType

typedef Superclass::JacobianType itk::KernelTransform2< TScalarType, NDimensions >::JacobianType;

typedef InputPointType

typedef Superclass::InputPointType itk::KernelTransform2< TScalarType, NDimensions >::InputPointType;

typedef OutputPointType

typedef Superclass::OutputPointType itk::KernelTransform2< TScalarType, NDimensions >::OutputPointType;

typedef InputVectorType

typedef Superclass::InputVectorType itk::KernelTransform2< TScalarType, NDimensions >::InputVectorType;

typedef OutputVectorType

typedef Superclass::OutputVectorType itk::KernelTransform2< TScalarType, NDimensions >::OutputVectorType;

typedef InputCovariantVectorType

typedef Superclass::InputCovariantVectorType itk::KernelTransform2< TScalarType, NDimensions >::InputCovariantVectorType;

typedef OutputCovariantVectorType

typedef Superclass::OutputCovariantVectorType itk::KernelTransform2< TScalarType, NDimensions >::OutputCovariantVectorType;

typedef InputVnlVectorType

typedef Superclass::InputVnlVectorType itk::KernelTransform2< TScalarType, NDimensions >::InputVnlVectorType;

typedef OutputVnlVectorType

typedef Superclass::OutputVnlVectorType itk::KernelTransform2< TScalarType, NDimensions >::OutputVnlVectorType;

typedef NonZeroJacobianIndicesType

typedef Superclass::NonZeroJacobianIndicesType itk::KernelTransform2< TScalarType, NDimensions >::NonZeroJacobianIndicesType;

AdvancedTransform typedefs.

typedef SpatialJacobianType

typedef Superclass::SpatialJacobianType itk::KernelTransform2< TScalarType, NDimensions >::SpatialJacobianType;

typedef JacobianOfSpatialJacobianType

typedef Superclass::JacobianOfSpatialJacobianType itk::KernelTransform2< TScalarType, NDimensions >::JacobianOfSpatialJacobianType;

typedef SpatialHessianType

typedef Superclass::SpatialHessianType itk::KernelTransform2< TScalarType, NDimensions >::SpatialHessianType;

typedef JacobianOfSpatialHessianType

typedef Superclass::JacobianOfSpatialHessianType itk::KernelTransform2< TScalarType, NDimensions >::JacobianOfSpatialHessianType;

typedef InternalMatrixType

typedef Superclass::InternalMatrixType itk::KernelTransform2< TScalarType, NDimensions >::InternalMatrixType;

typedef PointSetTraitsType

typedef DefaultStaticMeshTraits< TScalarType, NDimensions, NDimensions, TScalarType, TScalarType > itk::KernelTransform2< TScalarType, NDimensions >::PointSetTraitsType;

PointList typedef. This type is used for maintaining lists of points, specifically, the source and target landmark lists.

typedef PointSetType

typedef PointSet< InputPointType, NDimensions, PointSetTraitsType > itk::KernelTransform2< TScalarType, NDimensions >::PointSetType;

typedef PointSetPointer

typedef PointSetType::Pointer itk::KernelTransform2< TScalarType, NDimensions >::PointSetPointer;

typedef PointsContainer

typedef PointSetType::PointsContainer itk::KernelTransform2< TScalarType, NDimensions >::PointsContainer;

typedef PointsIterator

typedef PointSetType::PointsContainerIterator itk::KernelTransform2< TScalarType, NDimensions >::PointsIterator;

typedef PointsConstIterator

typedef PointSetType::PointsContainerConstIterator itk::KernelTransform2< TScalarType, NDimensions >::PointsConstIterator;

typedef VectorSetType

typedef VectorContainer< unsigned long, InputVectorType > itk::KernelTransform2< TScalarType, NDimensions >::VectorSetType;

VectorSet typedef.

typedef VectorSetPointer

typedef VectorSetType::Pointer itk::KernelTransform2< TScalarType, NDimensions >::VectorSetPointer;

typedef IMatrixType

typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > itk::KernelTransform2< TScalarType, NDimensions >::IMatrixType;

'I' (identity) matrix typedef.

typedef GMatrixType

typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > itk::KernelTransform2< TScalarType, NDimensions >::GMatrixType;

'G' matrix typedef.

typedef LMatrixType

typedef vnl_matrix< TScalarType > itk::KernelTransform2< TScalarType, NDimensions >::LMatrixType;

'L' matrix typedef.

typedef KMatrixType

typedef vnl_matrix< TScalarType > itk::KernelTransform2< TScalarType, NDimensions >::KMatrixType;

'K' matrix typedef.

typedef PMatrixType

typedef vnl_matrix< TScalarType > itk::KernelTransform2< TScalarType, NDimensions >::PMatrixType;

'P' matrix typedef.

typedef YMatrixType

typedef vnl_matrix< TScalarType > itk::KernelTransform2< TScalarType, NDimensions >::YMatrixType;

'Y' matrix typedef.

typedef WMatrixType

typedef vnl_matrix< TScalarType > itk::KernelTransform2< TScalarType, NDimensions >::WMatrixType;

'W' matrix typedef.

typedef DMatrixType

typedef vnl_matrix< TScalarType > itk::KernelTransform2< TScalarType, NDimensions >::DMatrixType;

'D' matrix typedef. Deformation component

typedef AMatrixType

typedef vnl_matrix_fixed< TScalarType, NDimensions, NDimensions > itk::KernelTransform2< TScalarType, NDimensions >::AMatrixType;

'A' matrix typedef. Rotational part of the Affine component

typedef BMatrixType

typedef vnl_vector_fixed< TScalarType, NDimensions > itk::KernelTransform2< TScalarType, NDimensions >::BMatrixType;

'B' matrix typedef. Translational part of the Affine component

typedef RowMatrixType

typedef vnl_matrix_fixed< TScalarType, 1, NDimensions > itk::KernelTransform2< TScalarType, NDimensions >::RowMatrixType;

Row matrix typedef.

typedef ColumnMatrixType

typedef vnl_matrix_fixed< TScalarType, NDimensions, 1 > itk::KernelTransform2< TScalarType, NDimensions >::ColumnMatrixType;

Column matrix typedef.

Protected Types Documentation

typedef SVDDecompositionType

typedef vnl_svd< ScalarType > itk::KernelTransform2< TScalarType, NDimensions >::SVDDecompositionType;

Decompositions, needed for the L matrix. These decompositions are cached for performance reasons during registration. During registration, in every iteration SetParameters() is called, which in turn calls ComputeWMatrix(). The L matrix is not changed however, and therefore it is not needed to redo the decomposition.

typedef QRDecompositionType

typedef vnl_qr< ScalarType > itk::KernelTransform2< TScalarType, NDimensions >::QRDecompositionType;

Public Functions Documentation

function itkTypeMacro

itkTypeMacro(
    KernelTransform2 ,
    AdvancedTransform 
)

Run-time type information (and related methods).

function itkNewMacro

itkNewMacro(
    Self 
)

New macro for creation of through a Smart Pointer.

function itkStaticConstMacro

itkStaticConstMacro(
    SpaceDimension ,
    unsigned int ,
    NDimensions 
)

Dimension of the domain space.

function GetNumberOfParameters

inline virtual NumberOfParametersType GetNumberOfParameters(
    void 
) const

Return the number of parameters that completely define the Transform.

function itkGetObjectMacro

itkGetObjectMacro(
    SourceLandmarks ,
    PointSetType 
)

Get the source landmarks list, which we will denote \( p \).

function SetSourceLandmarks

virtual void SetSourceLandmarks(
    PointSetType * 
)

Set the source landmarks list.

function itkGetObjectMacro

itkGetObjectMacro(
    TargetLandmarks ,
    PointSetType 
)

Get the target landmarks list, which we will denote \( q \).

function SetTargetLandmarks

virtual void SetTargetLandmarks(
    PointSetType * 
)

Set the target landmarks list.

function itkGetObjectMacro

itkGetObjectMacro(
    Displacements ,
    VectorSetType 
)

Get the displacements list, which we will denote \( d \), where \( d_i = q_i - p_i \).

function ComputeWMatrix

void ComputeWMatrix(
    void 
)

Compute W matrix.

function ComputeLInverse

void ComputeLInverse(
    void 
)

Compute L matrix inverse.

function TransformPoint

virtual OutputPointType TransformPoint(
    const InputPointType & thisPoint
) const

Compute the position of point in the new space

function TransformVector

inline virtual OutputVectorType TransformVector(
    const InputVectorType & 
) const

These vector transforms are not implemented for this transform.

function TransformVector

inline virtual OutputVnlVectorType TransformVector(
    const InputVnlVectorType & 
) const

function TransformCovariantVector

inline virtual OutputCovariantVectorType TransformCovariantVector(
    const InputCovariantVectorType & 
) const

function GetJacobian

virtual void GetJacobian(
    const InputPointType & ,
    JacobianType & ,
    NonZeroJacobianIndicesType & 
) const

Reimplements: itk::AdvancedTransform::GetJacobian

Compute the Jacobian of the transformation.

function SetIdentity

virtual void SetIdentity(
    void 
)

Set the Transformation Parameters to be an identity transform.

function SetParameters

virtual void SetParameters(
    const ParametersType & 
)

Set the Transformation Parameters and update the internal transformation. The parameters represent the source landmarks. Each landmark point is represented by NDimensions doubles. All the landmarks are concatenated to form one flat Array.

function SetFixedParameters

virtual void SetFixedParameters(
    const ParametersType & 
)

Set Transform Fixed Parameters: To support the transform file writer this function was added to set the target landmarks similar to the SetParameters function setting the source landmarks

function UpdateParameters

virtual void UpdateParameters(
    void 
)

Update the Parameters array from the landmarks coordinates.

function GetParameters

virtual const ParametersType & GetParameters(
    void 
) const

Get the Transformation Parameters - Gets the source landmarks.

function GetFixedParameters

virtual const ParametersType & GetFixedParameters(
    void 
) const

Get Transform Fixed Parameters - Gets the target landmarks.

function SetStiffness

inline virtual void SetStiffness(
    double stiffness
)

Stiffness of the spline. A stiffness of zero results in the standard interpolating spline. A non-zero stiffness allows the spline to approximate rather than interpolate the landmarks. Stiffness values are usually rather small, typically in the range of 0.001 to 0.1. The approximating spline formulation is based on the short paper by R. Sprengel, K. Rohr, H. Stiehl. "Thin-Plate Spline Approximation for Image Registration". In 18th International Conference of the IEEE Engineering in Medicine and Biology Society. 1996.

function itkGetMacro

itkGetMacro(
    Stiffness ,
    double 
)

function SetAlpha

inline virtual void SetAlpha(
    TScalarType  itkNotUsedAlpha
)

This method makes only sense for the ElasticBody splines. Declare here, so that you can always call it if you don't know the type of kernel beforehand. It will be overridden in the ElasticBodySplineKernelTransform and in the ElasticBodyReciprocalSplineKernelTransform.

function GetAlpha

inline virtual TScalarType GetAlpha(
    void 
) const

function itkSetMacro

itkSetMacro(
    PoissonRatio ,
    TScalarType 
)

This method makes only sense for the ElasticBody splines. Declare here, so that you can always call it if you don't know the type of kernel beforehand. It will be overridden in the ElasticBodySplineKernelTransform and in the ElasticBodyReciprocalSplineKernelTransform.

function GetPoissonRatio

inline virtual const TScalarType GetPoissonRatio(
    void 
) const

function itkSetMacro

itkSetMacro(
    MatrixInversionMethod ,
    std::string 
)

Matrix inversion by SVD or QR decomposition.

function itkGetConstReferenceMacro

itkGetConstReferenceMacro(
    MatrixInversionMethod ,
    std::string 
)

function GetSpatialJacobian

inline virtual void GetSpatialJacobian(
    const InputPointType & ipp,
    SpatialJacobianType & sj
) const

Reimplements: itk::AdvancedTransform::GetSpatialJacobian

Must be provided.

function GetSpatialHessian

inline virtual void GetSpatialHessian(
    const InputPointType & ipp,
    SpatialHessianType & sh
) const

Reimplements: itk::AdvancedTransform::GetSpatialHessian

Compute the spatial Hessian of the transformation.

The spatial Hessian is the vector of matrices of partial second order derivatives of the transformation components with respect to the spatial position \(x\), evaluated at a point \(p\).

with i the i-th component of the transformation.

function GetJacobianOfSpatialJacobian

inline virtual void GetJacobianOfSpatialJacobian(
    const InputPointType & ipp,
    JacobianOfSpatialJacobianType & jsj,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const

Reimplements: itk::AdvancedTransform::GetJacobianOfSpatialJacobian

Compute the Jacobian of the spatial Jacobian of the transformation.

The Jacobian of the spatial Jacobian is the derivative of the spatial Jacobian to the transformation parameters \(\mu\), evaluated at a point \(p\).

function GetJacobianOfSpatialJacobian

inline virtual void GetJacobianOfSpatialJacobian(
    const InputPointType & ipp,
    SpatialJacobianType & sj,
    JacobianOfSpatialJacobianType & jsj,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const

Reimplements: itk::AdvancedTransform::GetJacobianOfSpatialJacobian

Compute both the spatial Jacobian and the Jacobian of the spatial Jacobian of the transformation.

function GetJacobianOfSpatialHessian

inline virtual void GetJacobianOfSpatialHessian(
    const InputPointType & ipp,
    JacobianOfSpatialHessianType & jsh,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const

Reimplements: itk::AdvancedTransform::GetJacobianOfSpatialHessian

Compute the Jacobian of the spatial Hessian of the transformation.

The Jacobian of the spatial Hessian is the derivative of the spatial Hessian to the transformation parameters \(\mu\), evaluated at a point \(p\).

function GetJacobianOfSpatialHessian

inline virtual void GetJacobianOfSpatialHessian(
    const InputPointType & ipp,
    SpatialHessianType & sh,
    JacobianOfSpatialHessianType & jsh,
    NonZeroJacobianIndicesType & nonZeroJacobianIndices
) const

Reimplements: itk::AdvancedTransform::GetJacobianOfSpatialHessian

Compute both the spatial Hessian and the Jacobian of the spatial Hessian of the transformation.

Protected Functions Documentation

function KernelTransform2

KernelTransform2()

function ~KernelTransform2

virtual ~KernelTransform2()

function PrintSelf

void PrintSelf(
    std::ostream & os,
    Indent indent
) const

function ComputeG

virtual void ComputeG(
    const InputVectorType & landmarkVector,
    GMatrixType & GMatrix
) const

Reimplemented by: itk::ThinPlateSplineKernelTransform2::ComputeG

Compute G(x) This is essentially the kernel of the transform. By overriding this method, we can obtain (among others): Elastic body spline Thin plate spline Volume spline.

function ComputeReflexiveG

virtual void ComputeReflexiveG(
    PointsIterator ,
    GMatrixType & GMatrix
) const

Compute a G(x) for a point to itself (i.e. for the block diagonal elements of the matrix K. Parameter indicates for which landmark the reflexive G is to be computed. The default implementation for the reflexive contribution is a diagonal matrix where the diagonal elements are the stiffness of the spline.

function ComputeDeformationContribution

virtual void ComputeDeformationContribution(
    const InputPointType & inputPoint,
    OutputPointType & result
) const

Reimplemented by: itk::ThinPlateSplineKernelTransform2::ComputeDeformationContribution

Compute the contribution of the landmarks weighted by the kernel function to the global deformation of the space.

function ComputeK

void ComputeK(
    void 
)

Compute K matrix.

function ComputeL

void ComputeL(
    void 
)

Compute L matrix.

function ComputeP

void ComputeP(
    void 
)

Compute P matrix.

function ComputeY

void ComputeY(
    void 
)

Compute Y matrix.

function ComputeD

void ComputeD(
    void 
)

Compute displacements \( q_i - p_i \).

function ReorganizeW

void ReorganizeW(
    void 
)

Warning: This method release the memory of the W Matrix.

Reorganize the components of W into D (deformable), A (rotation part of affine) and B (translational part of affine ) components.

Public Attributes Documentation

variable m_SourceLandmarks

PointSetPointer m_SourceLandmarks;

The list of source landmarks, denoted 'p'.

variable m_TargetLandmarks

PointSetPointer m_TargetLandmarks;

The list of target landmarks, denoted 'q'.

Protected Attributes Documentation

variable m_Stiffness

double m_Stiffness;

Stiffness parameter.

variable m_Displacements

VectorSetPointer m_Displacements;

The list of displacements. d[i] = q[i] - p[i];

variable m_LMatrix

LMatrixType m_LMatrix;

The L matrix.

variable m_LMatrixInverse

LMatrixType m_LMatrixInverse;

The inverse of L, which we also cache.

variable m_KMatrix

KMatrixType m_KMatrix;

The K matrix.

variable m_PMatrix

PMatrixType m_PMatrix;

The P matrix.

variable m_YMatrix

YMatrixType m_YMatrix;

The Y matrix.

variable m_WMatrix

WMatrixType m_WMatrix;

The W matrix.

variable m_DMatrix

DMatrixType m_DMatrix;

The Deformation matrix. This is an auxiliary matrix that will hold the Deformation (non-affine) part of the transform. Those are the coefficients that will multiply the Kernel function.

variable m_AMatrix

AMatrixType m_AMatrix;

Rotational/Shearing part of the Affine component of the Transformation.

variable m_BVector

BMatrixType m_BVector;

Translational part of the Affine component of the Transformation.

variable m_WMatrixComputed

bool m_WMatrixComputed;

The G matrix. It used to be mutable because m_GMatrix was made an ivar only to avoid copying the matrix at return time but this is not necessary. SK: we don't need this matrix anymore as a member. Has the W matrix been computed?

variable m_LMatrixComputed

bool m_LMatrixComputed;

Has the L matrix been computed?

variable m_LInverseComputed

bool m_LInverseComputed;

Has the L inverse matrix been computed?

variable m_LMatrixDecompositionComputed

bool m_LMatrixDecompositionComputed;

Has the L matrix decomposition been computed?

variable m_LMatrixDecompositionSVD

SVDDecompositionType * m_LMatrixDecompositionSVD;

variable m_LMatrixDecompositionQR

QRDecompositionType * m_LMatrixDecompositionQR;

variable m_I

IMatrixType m_I;

Identity matrix.

variable m_NonZeroJacobianIndices

NonZeroJacobianIndicesType m_NonZeroJacobianIndices;

Precomputed nonzero Jacobian indices (simply all params)

variable m_NonZeroJacobianIndicesTemp

NonZeroJacobianIndicesType m_NonZeroJacobianIndicesTemp;

for old GetJacobian() method:

variable m_FastComputationPossible

bool m_FastComputationPossible;

The Jacobian can be computed much faster for some of the derived kerbel transforms, most notably the TPS.


Updated on 2024-07-12 at 20:10:34 +0000